Abstract
The electron structure and physical properties of strongly correlated systems containing elements with unfilled 3d, 4d, and 5f shells are analyzed. These systems include several transition metals, rare-earth elements, and actinides, as well as their numerous compounds, such as various oxides exhibiting metal–insulator phase transitions, cuprates, manganites, f systems with heavy fermions, and Kondo insulators. It is shown that the low-energy physics of such systems is described by three basic models: the Hubbard model, the sd-exchange model, and the periodic Anderson model under the condition that the on-site Coulomb repulsion energy U or the sd exchange energy J is of the order of the conduction-band width W. This situation does not involve a small parameter and should be treated nonperturbatively. We describe one such approach, the dynamic mean-field theory (DMFT), in which a system is considered to be only dynamically but not spatially correlated. We show that this approach, which is fully justified in the limit of large spatial dimensions (d→∞), covers the entire physics of strongly correlated systems and adequately describes the phenomena they exhibit. Extending the DMFT to include spatial correlations enables various d and f systems to be quantitatively described. Being a subject of intense development in recent years, the DMFT is the most effective and universal tool for studying various strongly correlated systems.
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